Partial functional linear models are widely studied and applied models, where the response variable is related to both general random variables and functional random variables. However, with the increasing application of data scenarios involving functional and vector-valued covariates and scalar responses in modern science, this paper proposes a partial functional regression model based on Gaussian processes. On the one hand, the proposed method can flexibly fit the nonlinear connection relationship between the functional covariates and the scalar responses by assuming the existence of a Gaussian process prior between them. On the other hand, for vector-valued covariates, in this paper, while constructing the linear relationship between them and scalar responses, the LASSO regularization technique is used to achieve the purpose of variable selection. Furthermore, in this paper, functional principal component analysis is used as the regularization strategy to approximate the distances between random functions, thereby achieving the approximate calculation of the kernel function matrix. The simulation experiment analysis indicates that the proposed method has higher prediction accuracy compared with the benchmark model and can effectively identify irrelevant variables. The actual data analysis also confirmed the comprehensive performance of the proposed method.